Question:
In a triangle ABC, AB = 15 cm, BC = 13 cm and AC = 14 cm. Find the area of triangle ABC and hence its altitude on AC.
Solution:
Let the sides of the given triangle be AB = a, BC = b, AC = c respectively.
So given,
a = 15 cm
b = 13 cm
c = 14 cm
By using Heron's Formula
The Area of the triangle $=\sqrt{s \times(s-a) \times(s-b) \times(s-c)}$
Semi perimeter of a triangle = 2s
2s = a + b + c
s = (a + b + c)/2
s = (15 + 13 + 14)/2
s = 21 cm
Therefore,
Area of the triangle $=\sqrt{s \times(s-a) \times(s-b) \times(s-c)}$
$=\sqrt{21 \times(21-15) \times(21-13) \times(21-14)}$
$=84 \mathrm{~cm}^{2}$
BE is a perpendicular on AC
Now, area of triangle = 84 cm2
1/2 × BE × AC = 84 cm2
BE = 12 cm
The length of BE is 12 cm
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- JEE Main
- Exam Pattern
- Previous Year Papers
- PYQ Chapterwise
- Physics
- Kinematics 1D
- Kinemetics 2D
- Friction
- Work, Power, Energy
- Centre of Mass and Collision
- Rotational Dynamics
- Gravitation
- Calorimetry
- Elasticity
- Thermal Expansion
- Heat Transfer
- Kinetic Theory of Gases
- Thermodynamics
- Simple Harmonic Motion
- Wave on String
- Sound waves
- Fluid Mechanics
- Electrostatics
- Current Electricity
- Capacitor
- Magnetism and Matter
- Electromagnetic Induction
- Atomic Structure
- Dual Nature of Matter
- Nuclear Physics
- Radioactivity
- Semiconductors
- Communication System
- Error in Measurement & instruments
- Alternating Current
- Electromagnetic Waves
- Wave Optics
- X-Rays
- All Subjects
- Physics
- Motion in a Plane
- Law of Motion
- Work, Energy and Power
- Systems of Particles and Rotational Motion
- Gravitation
- Mechanical Properties of Solids
- Mechanical Properties of Fluids
- Thermal Properties of matter
- Thermodynamics
- Kinetic Theory
- Oscillations
- Waves
- Electric Charge and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Thermoelectric Effects of Electric Current
- Heating Effects of Electric Current
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Wave
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Atoms
- Nuclei
- Semiconductor Electronics: Materials, Devices and Simple Circuits.
- Chemical Effects of Electric Current,
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